The interactions between orthodontic treatment and craniofacial growth are ill-understood, since treatment is an adjustment superimposed on unaltered growth which we cannot observe. To these problems we shall apply certain new tensor metrics for shape change, which embody growth rates in all regions and directions simultaneously. From an extensive computerized data base of longitudinal cephalographic series on untreated children, we will compute tensor measures of growth during various age intervals. We will then identify, using tensor statistics, the best predictors of future growth from tensor measures of individual cephalograms in a series. For patients entering treatment, for whom no earlier records are available, we will estimate expected growth from features of initial cephalograms. Treatment effect is then measured as the contrast predicted and observed growth, another tensor field. We may then study its statistical properties directly as a function of patient's age and sex and of the various modalities of intervention.